Neutral and volatility strategies

OpeningBeing right on direction doesn’t help

The stock is at $100 and IV is 30%. You think big news is coming next month, but you can’t tell whether it will be good or bad, so you buy a 30-day straddle at the 100 strike: one call plus one put, for $6.85 in total.

Whether this trade makes money has nothing to do with up or down. All that matters is how far the stock is from 100 at expiration:

If the stock rises to 103, you were right that it would go up, and you still lose $385. You only make money if the stock ends up outside the range of 93.15 to 106.85. So where does the ±6.85 hurdle come from? It is roughly the “average move” the market expects. At 30 days and 30% IV, a one-standard-deviation move is 100 × 0.30 × √(30/365) = 8.60, and the average absolute move is 0.8 times one standard deviation: 0.8 × 8.60 = 6.88.

So buying a straddle is a bet against the market: “The stock will actually move more than the average move you have priced in.” Selling a straddle is the opposite bet. Every strategy in this chapter is a different package for this one bet.

9.1What volatility strategies bet on

Volatility strategies shrink the effect of direction to very little. The bet that remains is one of two kinds: whether realized or implied volatility turns out larger, or whether implied volatility itself rises or falls.

• Realized vs implied: if you hold to expiry, or delta-hedge while you hold, your P&L is set by Gamma and Theta (Chapter 4, Section 4.6). The buyer needs realized volatility to be larger; the seller needs it to be smaller.
• Changes in implied volatility: if you close before expiry, P&L is driven mainly by Vega. If IV rises after you buy, you can make money even if the stock hasn’t moved; if IV falls after you sell, the same is true.

When you read this table, look at the signs of Gamma and Theta first: they are always opposite. Positive-Gamma structures (long straddle, long strangle) pay Theta every day; negative-Gamma structures (iron condor, iron butterfly, butterfly, calendar) collect Theta every day. The calendar is the only structure that is “negative Gamma, positive Vega”: it fears a big move in the stock but welcomes a rise in IV, which gives it a special use around earnings (Section 9.4).

Time to expiry decides whether you are betting on Gamma or Vega

Even for the same long ATM straddle, the time to expiry decides what you are mainly betting on. Per $1 of premium, every expiration has the same sensitivity to IV: an ATM straddle’s price is proportional to σ, so each 1-point rise in IV lifts the price by about 1 ÷ 30 = 3.3%. Gamma is another story. A 7-day straddle (3.31) carries 0.058 of Gamma per dollar of premium; a 180-day straddle (16.69) carries only 0.0022, a 26-fold difference. So a short-dated straddle is a Gamma bet, a bet that the stock moves a lot over the next few days. A long-dated straddle is a Vega bet: it barely responds to short-term realized volatility, and its P&L depends mainly on changes in IV. The same goes for sellers: selling a short-dated structure sells Gamma, and selling a long-dated structure sells Vega.

9.2Straddles and strangles

A straddle buys a big move in either direction; a strangle trades a lower cost for breakevens that are farther away. Selling them means collecting that insurance premium and carrying the tails on both sides.

• Straddle: a call plus a put with the same strike and the same expiration, usually at the money.
• Strangle: an OTM put plus an OTM call, with two separate strikes.

A few patterns:

• The cheaper it is, the worse your odds. The 90/110 strangle costs only $1.06, but the stock has to move more than 11% for it to make money, which the market prices at only about a 20% chance. Buyers are often drawn in by “cheap” and forget that it is cheap because it is hard to win.
• Expectancy depends only on realized volatility. When realized volatility equals IV, all three have an expectancy of 0; at 35% realized they are all positive, and at 25% they are all negative. The structure changes how often you win and how much you win, but not the bet itself.
• Gamma per dollar: the straddle buys about 0.013 of Gamma per dollar of premium, the 95/105 strangle about 0.026, and the 90/110 about 0.045. OTM structures have more leverage, but their Gamma only pays off when the stock gets near a strike.

Selling straddles and strangles: no floor on either side

The seller collects the cost in the table as premium, and the risk flips over symmetrically: on the call side the loss has no upper limit, and on the put side it runs until the stock goes to zero. On a ±10% or ±20% jump the next day (assuming IV rises to 45%), a short 100 straddle comes out at −$569 / −$679 and −$1,321 / −$1,435, and a short 90/110 strangle at −$367 / −$496 and −$975 / −$1,138. The strangle loses somewhat less, but it also collects only one-sixth of the straddle’s premium. The position-sizing rules from Chapter 8 apply here too: size by the gap loss, not by margin.

The other way a long straddle pays: rising IV

Hold to expiry and you are betting on realized volatility; close early and you are betting on IV. A 45-day ATM straddle costs 8.39, with Vega of $27.88 per point. 10 days later the stock is still at 100. If IV is unchanged, the straddle is worth 7.40 and you lose $99 per contract: that is Theta. If IV rises to 33%, you lose $25; to 36%, you make $49; to 40%, you make $147. In other words, IV has to rise to about 34% within those 10 days just to offset the time decay.

The typical setup for this trade: a known event (earnings, a product launch, a regulatory ruling) is a few weeks away, and front-month IV hasn’t started to climb yet. If you sell after IV has risen but before the event, you never carry the jump from the event itself. The risk is that IV doesn’t rise while Theta takes its cut every day. And the market often prices things in early: by the time you notice IV “hasn’t risen yet,” it may already have (Chapter 10).

9.3Iron condors, iron butterflies and butterflies

Add two “wings” to a short strangle or a short straddle and you get the iron condor and the iron butterfly, whose maximum loss is fixed. The wing width decides how much premium you trade for how much tail protection.

• Iron condor: a put credit spread + a call credit spread. Example: sell the 91 put, buy the 86 put, sell the 112 call, buy the 117 call.
• Iron butterfly: sell an ATM straddle, then buy OTM options the same distance away on each side. Example: sell the 100 straddle, buy the 95 put and the 105 call.
• Butterfly: all calls (or all puts). Buy 1 at the lower strike, sell 2 in the middle, buy 1 at the higher strike, and pay a debit.

Wing width: how much insurance to buy

With the short strikes unchanged, the probability of a “full profit” is 67.3% for all three wing widths (the stock stays between 91 and 112). The wider the wings, the cheaper and farther away the insurance you buy, the more premium you collect, and the slightly higher your probability of profit; the price is a maximum loss that grows several times over. In a gap, a condor with $10 wings is almost a strangle. Theta per contract is +$1.55, +$2.50 and +$4.25 per day, and Vega is −$4.73, −$7.58 and −$12.86 per point: the wider the wings, the closer you get to a naked short strangle.

The order of choices: first set your maximum-loss budget for one trade (Section 8.8), then choose the wing width, and finally divide the budget by the maximum loss per contract to get the number of contracts. With wings too narrow ($1–2), the premium is so small that commissions and the bid–ask spread eat almost all of it; with wings too wide, the iron condor loses its point as a defined-risk trade.

Iron butterflies and butterflies: two ways to build the same shape

Selling a 45-day 95/100/105 iron butterfly collects 4.05, with a maximum loss of 0.95 and breakevens at 95.95 / 104.05; at market pricing, the probability of profit is only 30.0%. Widen the wings to 10 (90/100/110) and you collect 6.44, with a maximum loss of 3.56 and a 45.9% probability of profit. The iron butterfly has a low probability of profit and a high payoff ratio; it makes money when the stock gets “pinned” in the middle.

Buying the 95/100/105 call butterfly costs 0.925, with a maximum profit of 4.075 and breakevens at 95.93 / 104.07. Its payoff at expiry is exactly the same as the iron butterfly’s: 5 × e^−rT − 0.925 = 4.05, which is exactly the premium the iron butterfly collects. One takes in money and one pays it out, but the shape is the same. Which one to use depends on liquidity and capital. The butterfly uses only calls, so the 95 leg is in the money and usually has a wider bid–ask spread; all four legs of the iron butterfly are at or out of the money, so it fills more easily. The butterfly ties up only its debit, while the iron butterfly freezes margin equal to its maximum loss. If the stock sits near the middle strike at expiry, either one can be assigned and leave you with a stock position, so it is best to close before expiration.

Management, and adjusting in a trend

• Short-leg Delta: 0.10–0.20 is common. 0.16 is about one standard deviation out and balances premium against room for error.
• Taking profits: the 50% profit target and the 21-day rule from Chapter 8 apply here too. Because its profit zone is narrow, the iron butterfly usually takes profits at around 25%.
• The tested side: once a short leg’s Delta rises above 0.30, or the price touches the short strike, decide whether to close, roll or do nothing.
• The rule in a trend: in a trend, “tightening” an iron condor (moving the untested side toward the price) collects more premium, but makes both sides easier to hit. Before you adjust, ask yourself: if I had no position today, would I open this new one? Case 3 compares three choices with numbers.

9.4Calendar and diagonal spreads

A calendar spread sells the front month and buys the back month, and earns the front month’s faster time decay. It needs the stock to stay near the strike and back-month IV not to fall sharply.

Same strike, different expirations: sell the 30-day 100 call for 3.591, buy the 60-day 100 call for 5.168, for a net debit of 1.577. The front-month option has more Theta and loses value faster every day; the back month has more Vega and is more sensitive to IV. So a calendar is positive Theta, positive Vega, negative Gamma: the passage of time and a rise in IV help it, and a big move in the stock hurts it.

With IV unchanged, the profit zone runs from about 95.2 to 105.9, and if the stock sits exactly at 100 you make 2.01, more than the cost. The maximum loss approaches the 1.577 you paid: when the stock moves far away, both options turn into pure intrinsic value or become worthless, and the spread goes to 0. Each 5-point change in back-month IV moves the P&L near the strike by about 0.57; the farther from the strike, the smaller the effect.

Earnings calendars: sell the expensive front month, buy the cheap back month

Before earnings, IV on the nearest expiration that includes the earnings date gets pushed up a lot, while the back month rises only a little. You can see why by breaking out the “event variance” (Chapter 6, Section 6.8):

Suppose normal volatility is 30% and the expected earnings-day move is e = 7%. IV for the 7-day expiration is √(0.30² + 0.07² × 365/7) = 58.8%, and IV for the 35-day expiration is √(0.30² + 0.07² × 365/35) = 37.6%. Once earnings are out, the event variance disappears and both expirations go back to around 30%: front-month IV drops 29 points, the back month only 8. A calendar that sells the front month and buys the back month is collecting this difference.

Case 2 works through the full numbers. A calendar’s maximum loss is about the debit you paid, which makes it a good fit for expressing, in small size, the view that “the actual jump on this earnings report will be smaller than the market expects.”

Choosing expirations: the front month is usually 1–5 weeks out, and the back month 3–8 weeks beyond it. The farther out the back month, the larger its Vega and the more the calendar behaves like a plain long-IV position, while the Theta difference between the two legs matters less. With the back month too close, the Theta difference is too small to be worth paying the bid–ask spread twice. Also check whether the back month includes another big event (such as the next earnings report or a Fed meeting). If it does, that event will hold up back-month IV, and you are in effect also long volatility on the next event, which may not be what you want.

Diagonal spreads: calendars with different strikes

The two legs of a diagonal spread have different expirations and different strikes. One common version uses a deep-ITM back-month call in place of stock for a covered call: buy the 90-day 90 call (12.65, Delta 0.80), sell the 30-day 105 call (1.66, Delta 0.31), for a net debit of 10.99 and a net Delta of 0.49. Compared with the covered call in Section 8.2, the capital drops from $10,000 to about $1,099. The costs: if the stock falls, the loss on the back-month call can be larger than the cushion from the premium; if the stock rallies hard, the front-month call goes deep in the money, total profit is capped, and it can even come in below what you expected because the back month doesn’t have enough time value left. Diagonals are also common around earnings: sell the expensive front month, buy the cheap back month, and use the strikes to express a bit of direction.

9.5Keeping Delta neutral: frequency and cost

Hedging frequency changes how much your P&L swings, not its expectancy. The more often you hedge, the closer the result gets to the underlying bet of “realized minus implied volatility,” and the higher the cost.

A neutral structure’s Delta is close to zero only at the moment you open it. Once the stock moves, Gamma pushes Delta away. For 10 short ATM straddles, after the stock rises $1.57 (one daily standard deviation), Delta goes from −65 shares to −207 shares (Gamma is about −92.5 shares per dollar). Should you hedge back to zero, and how often? The simulation below answers that.

Setup: sell 10 contracts of a 30-day ATM straddle (collecting $6,854) and hedge with stock; check 4 times a day; trading cost $0.02 per share; 2,000 random paths (seed 99).

• The premium sets the expectancy. With no premium, every hedging method averages close to 0, and the differences are basically trading costs (the standard error for no hedge is about $116). With a premium, they all come in around +$1,000.
• Hedging compresses the swings. Without hedging the standard deviation is $5,201; hedging four times a day cuts it to $541. In the case with a premium, hedging four times a day makes 95% of paths profitable (5th percentile +$203), while without hedging 5% of paths lose more than $7,000.
• Thresholds are cheaper than a fixed schedule. A ±100-share threshold uses about two-thirds of the trading volume and gets close to the stability of “four times a day.” In practice, market makers mostly hedge on thresholds or on bands set by Gamma, not by the clock.

How do you set the threshold? A simple reference is “how much Delta changes on a one-daily-standard-deviation move,” which is |Γ| × S × σ ÷ √365. For the 10 straddles that is 92.5 × 100 × 0.30 ÷ 19.1 ≈ 145 shares. In the table, ±100 shares is about 0.7 daily standard deviations and ±300 shares about 2. A threshold between 0.5 and 1 daily standard deviation is a common compromise between variance and cost. Gamma grows as expiration approaches, so the number of shares the threshold corresponds to needs to be recomputed as you go.

For individual traders, the lesson of this table is this: if you sell volatility without hedging, what you mainly carry is directional risk, and the premium is only a small tilt in your favor. To make “selling volatility” live up to its name, either hedge, or use a defined-risk structure to cut off the directional risk. Adjusting with options is also a kind of hedge: selling a spread on the untested side or buying a small option in the same direction both pull Delta back, at the cost of changing the shape of the whole structure.

9.6When to buy and when to sell volatility

Look at three indicators together: where IV sits within its own history, the shape of the term structure, and the gap between realized and implied volatility. A bet is only worth making when all three point the same way.

Indicator 1: IV Rank

A low IV Rank means options are cheap relative to their own history, but “cheap” can last a long time, and low IV by itself doesn’t make IV rise. A high IV Rank means premiums are rich, but high IV usually has a reason: earnings, a lawsuit, a macro event. IV Rank tells you where the price is, not whether the price is right.

Indicator 2: the term structure

• Steeply upward-sloping (front-month IV clearly below the back month): common in calm markets. When you sell short-dated options, they “roll down” to lower IV as time passes, which helps the seller.
• Flat: front and back months are about the same. The market has no particular worry about the near term, and the seller gets no extra roll-down. A buyer gives up nothing by buying the back month here.
• Inverted (front month above the back month): the market is paying for risk right in front of it, which is common in panics and before events. This is when front-month premium is richest, but also when realized volatility is most likely to keep expanding.

Indicator 3: realized vs implied volatility

Compare realized volatility over the last 10–20 trading days with 30-day IV. If realized volatility stays above IV, options haven’t caught up with what is really going on, and buyers have the edge; if it stays below IV, the market is paying premium for volatility that isn’t happening, and sellers have the edge. “Stays” matters: one or two big days don’t count.

The thresholds are common starting points; calibrate them to each underlying’s own history. There is also one exception: before a known event (earnings, FOMC), high front-month IV is normal pricing, and IV Rank will read “high.” Whether that premium is worth selling depends on the historical distribution of event moves (Chapter 10), not on this table.

Three hypothetical examples:

• Stock A: IV Rank 15, flat term structure, 20-day realized volatility ÷ IV = 1.25, holding for two weeks now. All three items go to buyers, for a buyer total of +3: you can buy a straddle and hedge it with the thresholds from Section 9.5.
• Stock B: IV Rank 72, steeply upward-sloping term structure, ratio 0.70. A seller total of +3: sell an iron condor and size it with the gap test from Chapter 8.
• Stock C: IV Rank 88, inverted term structure, ratio 1.30. IV Rank gives sellers +1, and the other two items give buyers +1 each, for a buyer total of +1, short of +2: don’t trade, and wait for the inversion to clear. This is exactly the top-right cell of Figure 9-4: the moment the premium is most tempting is the moment the rules tell you to stand aside.

9.7Gamma scalping revisited

Buying a straddle and delta-hedging it isolates the bet on “realized vs implied volatility.” The expected daily P&L is about ½ Γ S² (σ²_realized − σ²_implied) ÷ 365.

Take the position from Chapter 4, Section 4.7: 10 contracts of a 30-day ATM straddle, Gamma about 92.5 shares per dollar, Theta about −$114 a day. By the formula, the expected daily P&L is +$88.7 at 40% realized volatility, +$41.2 at 35%, 0 at 30% and −$34.8 at 25%. The process, in review:

1. Buy a straddle when realized volatility looks likely to come in above IV (the top-left cell, Section 9.6).
2. When you open the position, hedge Delta to zero with stock.
3. Re-hedge on thresholds: sell stock when it rises, buy stock when it falls (Section 9.5).
4. Record realized volatility every day and compare it with the IV you bought at.
5. Exit when realized volatility falls back below IV, or when IV jumps (you can sell the Vega gain).

For the full five-day walkthrough, see Chapter 4, Section 4.7. The simulation in Section 9.5 is its mirror image: sell a straddle and hedge it, and you earn the amount by which realized volatility falls short of implied. That is a market maker’s everyday business.

The difference between hedging and not hedging is what you are “watching.” An unhedged straddle only cares how far the stock is from the strike at the moment of expiry; a hedged straddle cares about the volatility accumulated along the whole path. In scenario A of Chapter 4, the stock swung back and forth sharply and ended up almost where it started: holding only the straddle lost $304, while hedging every day made $797. If your view is “it will swing violently but may not trend,” hedging is the way to cash in on that view.

CasesThree cases

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